Based on GroupâSubgroup Transformations - ACS Publications

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Phase Transition Mechanisms in LixCoO2 (0.25 ≤ x ≤ 1) Based on Group−Subgroup Transformations Hamdi Ben Yahia,* Masahiro Shikano,* and Hironori Kobayashi Research Institute for Ubiquitous Energy Devices, National Institute of Advanced Industrial Science and Technology (AIST), 1-8-31 Midorigaoka, Ikeda, Osaka 563-8577, Japan S Supporting Information *

ABSTRACT: The basic structural chemistry of O3−LixCoO2 (0.25 ≤ x ≤ 1) oxides is reviewed. Crystal chemical details of selected compositions and group−subgroup schemes are discussed with respect to phase transitions upon electrochemical or chemical deintercalation of the lithium atoms. Furthermore, the theoretical crystal structures of LixCoO2 supercells (x = 0.75, 0.5, 0.33, and 0.25) are reported for the first time based on the combination of transmission electron microscopy (TEM) and X-ray (XRD) or neutron diffraction (ND) experiments. Li0.75CoO2 and Li0.25CoO2 supercells crystallize with the space group R3̅m, a4 = 5.6234 Å and 5.624 Å, and c4 = 14.2863 Å and 14.26 Å, respectively, whereas the Li0.5CoO2 supercell crystallizes with the space group P21/m, a7 = 4.865 Å, b7 = 2.809 Å, c7 = 9.728 Å, and β7 = 99.59°. The Li0.33CoO2 supercell may crystallize in different unit cells (hexagonal or orthorhombic or monoclinic). For Li0.75CoO2, the TEM superstructure reflections are due to only one type of lithium and vacancy ordering within the lithium layers; however, for x = 0.5, the superstructure reflections are due to an intergrowth of two Li0.5CoO2 monoclinic structures (P2/m, a5 = 4.865(3) Å, b5 = 2.809(3) Å, c5 = 5.063(3) Å, β5 = 108.68(5)°) with the lithium and vacancies alternating the 1g and 1f atomic positions, in two successive layers, along the c direction. For Li0.33CoO2, in most cases, the Li and vacancy ordering are similar to Li and Mn ordering in the Li2MnO3 structure. The phase transition mechanisms from O3−LiCoO2 to O3−Li0.25CoO2 and from O3−LiCoO2 to spinel−Li0.5CoO2 have been determined, and the structural relationship between O3−LiCoO2 and Li2MnO3 has been discussed in detail. KEYWORDS: O3−LixCoO2 system, group−subgroup schemes, phase transition, lithium battery

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INTRODUCTION LiCoO2 was first synthesized by Johnston et al.1 in 1958. In 1980, Mizushima et al. reported its interesting electrochemical properties and its possible use for practical application.2 It was only in 1991 that Sony Corporation released the first commercial secondary battery consisting of LiCoO2 as a positive electrode and graphite as a negative electrode.3 Presently, O3−LiCoO2 is the most commonly used positive electrode material in lithium rechargeable batteries, which are widely used as a power source for portable electronic devices such as computers and mobile phones. Moreover, they have been intensively studied for use as power supplies of electric vehicles (EVs) and hybrid electric vehicles (HEVs). High energy and high power densities are required for such devices. Although the theoretical capacity is 274 mAh/g, LixCoO2 gives in a commercial cell only a specific capacity of about 140 mAh/g, which corresponds to the extraction of 0.5 Li per LiCoO2. Indeed, an upper cutoff voltage of about 4.2 V with respect to Li metal is usually applied to prevent the capacity loss observed for x < 0.5. This capacity fade is caused by several phenomena such as a side reaction with the electrolyte at high voltage, structural instability, surface instability, or cobalt dissolution.4−7 The coated LiCoO2 electrode has shown superior cycling © 2013 American Chemical Society

behavior compared to pristine material. The improvement in the electrochemical performance in the coated positive electrode is ascribed to the suppression of cobalt dissolution and the nonuniform distribution of local strain by the coating layer (ref 8 and refs therein). It is however still unclear how the structural changes contribute to the capacity loss in LixCoO2. There have been only a few studies reporting the possible transformation of O3−LiCoO2 to the spinel structure during or after electrochemical cycling.9−13 O3−LiCoO2 is isostructural to α-NaFeO2 and has rhombohedral symmetry, space group R3̅m (no. 166), a1 = 2.8166 Å, and c1 = 14.0452 Å (hexagonal setting).1 Its structure contains ABC close-packed oxygen arrays, between which are stacked alternatively lithium and cobalt sheets. Lithium deintercalation from O3−LiCoO2 could be performed until the O1−CoO2 phase.14 This end member is isostructural to CdI2, space group P3̅m (no. 164), a1 = 2.822 Å, and c1 = 4.29 Å. In the O3−LixCoO2 system, several other structural changes have been observed upon lithium deintercalation and have been recently reviewed.15 Received: June 14, 2013 Revised: August 16, 2013 Published: August 19, 2013 3687

dx.doi.org/10.1021/cm401942t | Chem. Mater. 2013, 25, 3687−3701

Chemistry of Materials

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Figure 1. (a) Group−subgroup transformation for the spinel−Li0.5CoO2 structure and (b) isomorphic unit cell enlargement of the layered O3−LiCoO2 structure.

For the particular composition x = 0.5, at least four structural models have been proposed: (i) monoclinic symmetry, space group C2/m, a5 = 4.872 Å, b5 = 2.808 Å, c5 = 5.053 Å, and β5 = 107.89° (Powder XRD);16,17 (ii) monoclinic symmetry, space group P2/m, a ≈ a5, b ≈ b5, c ≈ c5, β ≈ β5 (TEM/single crystal XRD; ref 15 and refs therein); (iii) monoclinic symmetry, space group Pm, a ≈ a5, b ≈ b5, c ≈ 2c5, and β ≈ β5 (TEM);18 and (v) cubic symmetry, space group Fd3m ̅ , and a = 8.02 Å (TEM/ND).12,13 Nowadays, theoretical calculations are becoming an essential tool for the design of crystal structures of new materials and for the simulation and predictions of their physical properties. Currently, there is strong demand for accurate crystal structures of the LixCoO2 compositions, in order to simulate the X-ray absorption spectra of these materials. The present work is intended to overview all the crystal structures observed in the LixCoO2 system 0.25 ≤ x ≤ 1 for a better understanding of the transformation mechanisms involved during the electrochemical cycling of LiCoO2 and for a better simulation of the physical properties of these materials. On the basis of the experimental and theoretical results reported to date, transformation mechanisms from LiCoO2 to Li0.25CoO2 are proposed using simple group−subgroup transformations. 1. Structural Relationship between the O3−LiCoO2 and Li0.5CoO2 Spinel Structure. For an accurate determination of the phase transition mechanism from the O3−LiCoO2 layered structure (R3̅m, a1 = 2.8166 Å, and c1 = 14.0452 Å)1 to the Li0.5CoO2 spinel structure (Fd3̅m, a2 = 7.992 Å),19 it is necessary to find a supercell, common to both structures, in which the comparison of the atomic position would be simple. For this purpose, the use of group−subgroup schemes in the Bärnighausen formalism is the key. Starting from the spinel structure, it is possible to reduce the symmetry from the space group Fd3̅m (a2 = 7.992 Å) to R3̅m (a3 = 5.6512 Å, and c3 = 13.8426 Å), where a⃗3 = 1/2(b2⃗ − a⃗2), b3⃗ = 1/2(c2⃗ − b2⃗ ), and c3⃗ = (a2⃗ + b2⃗ + c2⃗ ). This transition (translationengleiche of index 4) induces a transformation of the atomic positions as depicted in Figure 1a. The obtained a3 cell parameter is approximately 2 × a1 of the O3−LiCoO2 structure. Therefore, an isomorphic enlargement of the O3−LiCoO2 unit cell, with space group R3̅m, a⃗4 = −2a1⃗ , b4⃗ = −2b1⃗ , and c4⃗ = c1⃗ , is needed for a possible comparison with the spinel structure. Starting from the O3−subcell structure, three additional atomic positions have been introduced by doubling a1 and b1 cell parameters and applying a translation of 1/2a⃗ to the initial atomic positions. This isomorphic transition of index 4 is depicted in Figure 1b. For our convenience, the cobalt atoms in the O3−LiCoO2 subcell are set at the 3a (0 0 0) instead of the

conventional 3b (0 0 1/2) atomic position. Consequently, the oxygen atoms lie at (0 0 0.26) instead of (0 0 0.24). In the different tables and structural views, a specific color has been attributed to each atomic position for a better labeling. The comparison of the atomic positions of the Li0.5CoO2 hexagonal spinel cell (HSC) and O3−LiCoO2 supercell (O3SC) shows that the O1 and O2 atomic positions (highlighted in red) are identical. This is in agreement with the fact that both structures are known to be built up of ABC close-packed oxygen arrays. The Co2 atomic positions in HSC and O3SC are also identical. The main difference concerns the Li and Co1 atomic positions. It is worth it to notice that the atomic positions of Li1 in O3SC and Co1 in HSC are identical. This suggests a migration of Co1 from the 3a (0 0 0) to 3b (0 0 1/2) atomic position, after the deintercalation of Li1 from the 3b atomic position. Furthermore, Li2 shifts from 9d (1/2 0 1/2) to 6c (0 0 1/8) after the deintercalation of 1/3 of Li2. On the basis of these observations, the most plausible transformation mechanisms from the O3−LiCoO2 to the spinel−Li0.5CoO2 are proposed. 2. Transformation Mechanism from O3−LiCoO2 to O3−Li0.75CoO2 Structure. Starting from the O3−LiCoO2 subcell (Figure 2a1), the extraction of 0.25 Li induces a transformation of the chemical formula to O3−Li0.75◻0.25CoO2 (◻: vacancy) and the formation of a supercell 2a1 × 2b1 × c1, due to the ordering of the Li atoms and vacancies within the Li layer. In the O3SC structure (Figure 2b1), Li1 and Li2 occupy the 3b (0.25Li) and 9d (0.75Li) atomic positions, respectively. Therefore, it is suggested that Li1 is extracted first (Figure 2c1). The evolution of a single lithium layer and of the O3−LixCoO2 structure are depicted in Figure 2a2, b2, and c2 and Figure 2a3, b3, and c3, respectively. The first transformation corresponds to the isomorphic enlargement of the O3−LiCoO2 unit cell (for details, see section 1), whereas the second transformation corresponds to the extraction of 0.25 lithium from the O3−LiCoO2 supercell. This ordering of lithium and vacancies (Figure 2c2) has been predicted by several researchers;20,21 however, since satellite reflections could not be observed on the XRD powder patterns of O3−Li0.75CoO2, these latter have been indexed similar to O3−LiCoO2 (R3̅m, a1 = 2.8166 Å, and c1 = 14.0452 Å).14,21,22 Unlike X-rays that only scatter from electrons, electron diffraction interacts with both nuclei and electrons. Therefore, electron diffraction is more sensitive to light elements like lithium. Consequently, satellite reflections should be revealed due to lithium and vacancies ordering in O3−Li0.75CoO2. Indeed, Clémonçon et al. have observed extra reflections which have been attributed to the formation of a supercell 2a1 × 2b1 × c1.23 3688



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Figure 2. Transformation mechanism from the O3−LiCoO2 subcell to the O3−Li0.75CoO2 supercell. The crystallographic data (1), the projection views perpendicular to the lithium layer (2), and the perspective views of the structures (3) are reported for the O3−LiCoO2 subcell (a), O3−LiCoO2 supercell (b), and O3−Li0.75CoO2 supercell (c).

symmetry is preserved for the composition O3−Li0.5CoO2 (Figure 3b). Starting from this point, only two steps are required to obtain the spinel structure [migration of Li2 then Co1 (mechanism I) or vice versa (mechanism II)]. Since the 9d (1/2 0 1/2) atomic position (Figure 3b) is only 2/3 occupied, the Li2 atoms shift to the 6c (0 0 1/8) atomic position (Figure 3c). Consequently, strong electrostatic repulsion occurs between the Li2 (black sphere) on the tetrahedral sites and the Co1 (pink sphere) on the neighboring octahedral sites of the cobalt layer (dLi2−Co1 = 1/8 × c4 = 1.75 Å). This induces the migration of Co1 from the 3a (0 0 0) to 3b (1/3 2/3 1/6) [equivalent to (0 0 1/2)] atomic position (Figure 3d) and, therefore, the formation of the rhombohedral spinel-Li0.5CoO2 structure with a hexagonal cell. This cell can be transformed to the cubic spinel cell using the relations a2⃗ = −1/3(4a4⃗ + 2b4⃗ − c4⃗ ), b2⃗ = 1/3(2a4⃗ − 2b4⃗ + c4⃗ ), and c2⃗ = 1/3(2a4⃗ + 4b4⃗ + c4⃗ ). A view of the geometric relationship between the hexagonal and the cubic cells is reported in Figure 3e3 and e4. Several theoretical calculations have been conducted to predict the diffusion pathway of lithium in the layered O3−Li0.5CoO2 structure. It has been concluded that the diffusion through the intermediate vacant tetrahedral sites is more favorable than the direct jump of Li between two octahedral sites.24−26 Similarly to Li, the migration of Co1 cannot occur by a direct jump from the 3a (0 0 0) to the 3b (1/3 2/3 1/6) atomic position. Since, Co2 at 9e (1/2 0 0) is closer to 3b (1/3 2/3 1/6) than Co1, we suggest first the migration of 1/3 of Co2 to 3b (1/3 2/3 1/6), then the migration of Co1 from 3a (0 0 0) to 9e (1/2 0 0) (Figure 4).

This is in perfect agreement with our predicted structural model. To our knowledge, this is the first paper reporting the atomic positions of the O3−Li0.75CoO2 supercell (Figure 2c1). It should be mentioned that the c1 cell parameter increases from 14.0452 to 14.2863 Å after the deintercalation of 0.25 Li from O3−LiCoO2, whereas a1 decreases only slightly from 2.8166 to 2.8117 Å. Therefore, the final cell parameters for the O3−Li0.75CoO2 supercell should be a4 = b4 = 5.6234 Å and c4 = 14.2863 Å. It is well-known that the composition LixCoO2 (0.75 < x < 0.93) corresponds to a mixture of two phases of compositions close to Li0.75CoO2 and Li0.93CoO2. Therefore, the LixCoO2 compositions (0.75 ≤ x ≤ 0.93) could be expressed as LixCoO2 ≈ y × Li0.75CoO2 + (1 − y) × Li0.93CoO2 with y = (0.93 − x)/ (0.93 − 0.75). This suggest that Li0.75CoO2 does not start to form at x = 0.75 but at x ≈ 0.93. This explains why only anomalies around x = 0.93 and x = 0.5 have been observed on the cell voltage vs x and the derivative −dx/dV vs x curves (x: composition).16 This is at the origin of the little attention that has been paid to the crystal structure of Li0.75CoO2 comparing to Li0.5CoO2. 3. Transformation Mechanism from O3−Li0.75CoO2 (R3̅m) to the Spinel−Li0.5CoO2 (Fd3̅m) Structure. The transformation of the O3−Li0.75CoO2 supercell (R3̅m) to the spinel− Li0.5CoO2 structure (Fd3̅m) may occur in few steps with two possible mechanisms (I and/or II). These mechanisms are detailed in Figures 3−6. If we consider that the extraction of 0.25Li from O3−Li0.75CoO2 induces a statistical disorder of lithium and vacancies at the Li2 atomic position, the rhombohedral 3689



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Figure 3. Transformation mechanism I from the O3−Li0.75CoO2 supercell (a) to the cubic spinel−Li0.5CoO2 cell (e). The transformation steps 1 to 4 correspond to the deintercalation of 0.25Li from the O3−Li0.75CoO2 supercell, the migration of Li from 9d to 6c, the migration of Co from 3a to 3b, and the transformation from the rhombohedral- to the cubic-symmetry, successively. The crystallographic data (1), the Li2 polyhedra (2), the projection views perpendicular to the lithium layer (3), and the perspective views of the structures (4) are reported. The red arrows correspond to the Co migration pathway (c4). The cubic and the hexagonal cells of the spinel Li0.5CoO2 structure are depicted in blue and black, respectively (e3 and e4).

Figure 4. The transformation mechanism I of the O3−Li0.5CoO2 supercell to the spinel−Li0.5CoO2 cell, which occurs in five steps: Li2 at 9d (1/2 0 1/2) → Li2 at 6c (0 0 1/8), Co1 at 3a (0 0 0) → T1, 1/3Co2 at 9e (1/2 0 0) → T2, Co1 at T1 → □ of Co2 at 9e (1/2 0 0), and 1/3Co2 at T2 → □ at 3b (1/3 2/3 1/6). The arrows (→) and □ correspond to the migration pathways and the vacancies, respectively. The cobalt migration mechanism from the 3a (0 0 0) (orange octahedron) to 3b (1/3 2/3 1/6) (colorless octahedron) atomic position involves two vacant tetrahedral sites (labeled T1 and T2) which share only an edge with the Li2 tetrahedral site. The atomic positions (1/3 2/3 1/6) and (0 0 1/2) are equivalent.

For mechanism II (Figures 5 and 6), it is suggested that 1/3 of Co2 migrates from 9e (1/2 0 0) to 3b (1/3 2/3 1/6) via the vacant tetrahedral site (T2). Since T2 shares a face with the

The diffusion of the cobalt atoms involves two vacant tetrahedral sites that share only an edge with the lithium tetrahedral sites. The detailed mechanism (I) is illustrated in Figure 4. 3690



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Figure 5. Transformation mechanism II from the O3−Li0.75CoO2 supercell (a) to the spinel−Li0.5CoO2 cell (e). The transformation steps 1 to 4 correspond to the deintercalation of 0.25Li from the O3−Li0.75CoO2 supercell, the migration of Co from 3a to 3b, the migration of Li from 9d to 6c, and the transformation from the rhombohedral- to the cubic-symmetry, successively. The crystallographic data (1), the Li2 polyhedra (2), the projection views perpendicular to the lithium layer (3), and the perspective views of the structures (4) are reported. The red arrows correspond to the Co migration pathway (b4). The cubic and the hexagonal cells of the spinel Li0.5CoO2 structure are depicted in blue and black, respectively (e3 and e4).

Figure 6. The transformation mechanism II of the O3−Li0.5CoO2 supercell to the spinel−Li0.5CoO2 cell, which occurs in five steps: 1/3Co2 at 9e (1/2 0 0) → T2, Li2 at 9d (1/2 0 1/2) → Li2 at 6c (0 0 1/8), 1/3Co2 at T2 → □ at 3b (1/3 2/3 1/6), Co1 at 3a (0 0 0) → T1, and Co1 at T1 → □ of Co2 at 9e (1/2 0 0). The arrows (→) and □ correspond to the migration pathways and the vacancies, respectively. The cobalt migration mechanism from the 3a (0 0 0) (orange octahedron) to 3b (1/3 2/3 1/6) (colorless octahedron) atomic position involves two vacant tetrahedral sites (labeled T1 and T2) which share only a face with the Li2 octahedral site. The atomic positions (1/3 2/3 1/6) and (0 0 1/2) are equivalent.

tetrahedral site T1. Finally, the hexagonal spinel is transformed to the cubic spinel cell as previously described in mechanism I. The detailed mechanism II is illustrated in Figures 5 and 6. Both mechanisms (I and II) are in agreement with the previous work of Choi and Manthiram. Indeed, these authors have

octahedral coordinated Li2 at 9d (1/2 0 1/2), a strong electrostatic repulsion occurs between Co2 and Li2. Therefore, Li2 shifts from the octahedron 9d (1/2 0 1/2) to the tetrahedron 6c (0 0 1/8), inducing a migration of Co1 from 3a (0 0 0) to the 1/3 vacant site of Co2 at 9e (1/2 0 0), via the neighboring 3691



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Figure 7. Transformation mechanism from the rhombohedral O3−Li0.75CoO2 (R3̅m) to the monoclinic O3−Li0.5CoO2 (C2/m-type I) structure. The crystallographic data (1), the projection views perpendicular to the lithium layer (2), and the projection views along the layers (3) are reported for the O3−Li0.75CoO2 supercell (a), O3−Li0.5CoO2 supercell (b), O3−Li0.5CoO2 subcell (c), and O3−Li0.5CoO2 monoclinic subcell (d).

discussed the transformation of the layered Li0.5MO2 phases to the spinel phase and pointed out the migration of the transition metal via vacant tetrahedral sites.27 However, it is still unclear which migrates first, Li from the octahedral to the tetrahedral sites or Co from the cobalt to the lithium layer. Perhaps both occur simultaneously under thermodynamic and/or electrochemical conditions specific to each transition metal. The observation of the spinel structure at the surface of extensively cycled LixCoO2 materials cannot be only due to a simple structural transition as described above, although for Li0.5CoO2, the spinel structure is thermodynamically more stable than the layered Li0.5CoO2 structure. Many complex electrode−electrolyte interface phenomena should be taken into account (oxygen loss, strains, microcracks, Co dissolution, etc.), since the spinel phase is often observed only on the surface but not in the bulk of the electrochemically cycled materials. One should pay particular attention to the composition of the spinel phase at the surface. In some cases, Co3O4 with the spinel structure may form due to the release of oxygen from the cathode material [LixCoO2 = xLiCoO2 + (1 − x)/3Co3O4 + (1 − x)/3O2]. In this case, mechanisms I and II are not involved. 4. Transformation Mechanism from O3−Li0.75CoO2 to Monoclinic O3−Li0.5CoO2 Structure. 4.1. From O3− Li0.75CoO2 (R3̅m) to Monoclinic O3−Li0.5CoO2 (C2/m-Type I).

Figure 8. Group−subgroup transformation from rhombohedral (R3̅m) to monoclinic (C2/m-typeI) to monoclinic (P2/m), for the O3− LiCoO2 structure.

In order to obtain the monoclinic structure O3−Li0.5CoO2 (C2/m-type I), only one transformation mechanism is possible. The extraction of 0.25Li from the O3−Li0.75CoO2 supercell 3692



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Figure 9. Transformation mechanism from the rhombohedral O3−Li0.75CoO2 (R3̅m) to the monoclinic O3−Li0.5CoO2 (P2/m) structure.

a5/b5 from √3 and of the monoclinic angle β5 from the value of 109.15°.21 One should point out that all the structures crystallizing with the C2/m space group have been refined on powder XRD data. Since XRD has a limited ability to detect Li due its low scattering power, it has been impossible to detect the Li and vacancy ordering in the O3−Li0.5CoO2 monoclinic phase, using this technique. Only single crystal XRD and transmission electron microscopy have been able to observe this phenomenon, which implies a loss of the centring translations and a decrease of the symmetry from the C2/m to P2/m space group (see next section and Figure 8).15,18 4.2. From O3−Li0.75CoO2 (R3̅m) to Monoclinic O3− Li0.5CoO2 (P2/m). Starting from the O3−Li0.75CoO2 supercell (Figure 9a), 0.25 Li has to be extracted in order to obtain the Li0.5CoO2 composition. This suggests that 1/3 of Li2 at the 9d atomic position should be extracted. From a structural point of view, this leads to the formation of empty rows in the lithium layers. Depending on the choice of the lithium to be extracted, these rows may run along the [100] or [010] or [110] directions of the hexagonal supercell, which give rise to three possible ordered lithium/vacancy schemes (figure 9b2). It is worth it to notice that the extraction of 0.25 Li from Li0.75CoO2 leads to the loss of the −3 rotoinversion axis, which induces a reduction of the symmetry. Indeed, the three ordered schemes can be described using a monoclinic cell with a Bravais lattice P. The structural

(Figure 7a) induces a statistical disorder of Li and vacancies over all the lithium sites (Li1 and Li2 atomic positions should be half occupied; Figure 7b). In this case, the structure can be described in the O3−Li0.5CoO2 subcell with the Li at 3b (0 0 1/2) atomic position, half occupied (Figure 7c). Since C2/m is a subgroup of the R3̅m space group, only a slight distortion may explain the symmetry reduction from hexagonal to monoclinic. This distortion is reflected by additional diffraction peaks which appear on the powder patterns of the monoclinic O3−Li0.5CoO2 phase.16,17 Figure 7d2 and d3 show the structural relationship between the hexagonal and monoclinic settings, where a5⃗ = 2a1⃗ + b⃗1, b5⃗ = −b1⃗ , and c5⃗ = −1/3(2a1⃗ + b1⃗ + c1⃗ ). The cell parameters of the monoclinic cell are deduced from the hexagonal subcell (R3̅m, aH = 2.8166 Å, and cH = 14.0452 Å) using the following equations: aM =

3 × aH = 4.8785 Å, bM = aH = 2.8166 Å, CH cM = = 4.9561 Å, and 3 sin βM CH βM = 180° − tan−1 = 109.15° 3 × aH

where aM = a5, aH = a1, and M and H denote the monoclinic and the hexagonal lattices, respectively. The distortion of the hexagonal cell can be followed by examining the deviations of 3693



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Figure 10. Construction of the monoclinic O3−Li0.5CoO2 (P21/m) supercell. (a) Determination of the atomic positions in the a5 × b5 × 2c5 supercell, using the P1 space group; (b) Li/vacancy ordering with an alternation of Li2/□ and Li3/□ in successive Li layers; (c) unit cell parameter transformation using the (100 01̅0 1̅01̅) matrix; (d) origin shift and new atomic position determination for the P21/m space group; and (e) cell parameters and atomic positions optimization based on the single crystal data of O3−Li0.5CoO2.28

relationship between the hexagonal and monoclinic settings is given by a5⃗ = −a4⃗ −1/2b4⃗ , b5⃗ = 1/2b4⃗ , and c5⃗ = −1/3(−a4⃗ − 1/2b4⃗ + c4⃗ ) (Figure 9c). The cell parameters of the monoclinic cell are deduced from the hexagonal supercell (R3̅m, aH = 5.6332 Å, and cH = 14.0452 Å) using the following equations: aM =

3 × aH = 4.8785 Å, bM = aH = 2.8166 Å, 2 CH = 4.9561 Å, and cM = 3 sin βM CH βM = 180° − tan−1 = 109.15° 3 × a H 2

Figure 11. View of the lithium and vacancies ordering in Li0.33CoO2. The black lines correspond to the O3−LiCoO2 (R3̅m, a1 = 2.8166 Å, and c1 = 14.0452 Å) unit cell. The green lines correspond to the √3a1 × √3a1 supercell reported for Li0.33CoO2 and Li0.33NiO2, and the blue lines correspond to the Li2MnO3 (C2/m-type V, a12 = 4.9261 Å ≈ a9, b12 = 8.5270 Å ≈ b9, c12 = 5.0280 Å, and β12 = 109.22°) unit cell. The gray and black circles correspond to the lithium atoms and vacancies for Li 0.33 CoO 2 and lithium and manganese atoms for Li 2 MnO 3 composition, respectively.

where aM = a5, aH = a4, and M and H denote the monoclinic and the supercell-hexagonal lattices, respectively. The cell parameters obtained by this transformation are in perfect agreement with the single crystal data of O3−Li0.5CoO2 prepared by chemical deintercalation of LiCoO2 single crystals (P2/m, a = 4.865(3) Å, b = 2.809(3) Å, c = 5.063(3) Å, β = 108.68(5)°).28 Only an origin shift has to be applied to the red cell (Figure 9c2) in order to obtain the same atomic positions as for the single crystal structure. The three ordered lithium/vacancy schemes depicted in Figure 9b2 may coexist. Using electron diffraction microscopy, Shao-Horn et al. have been able to reveal reflections associated with lithium and vacancy ordering from all three variants within individual monoclinic Li0.5CoO2 crystals.18 Contrary to ShaoHorn et al., who have considered these three variants as twin domains, Chiang et al. have considered ferroelastic domains.29 One should mention that P2/m is a subgroup of C2/m, which is a subgroup of R3̅m (Figure 8). The loss of the C centering translations (klassengleiche transition of index 2) induces the

doubling of the atomic positions. Therefore, in the ordered monoclinic O3−Li0.5CoO2 (P2/m) structure, the Li1 at 1g (1/2 0 1/2) or Li2 at the 1f (0 1/2 1/2) atomic position should be empty. In the case where the Li1 at 1g (1/2 0 1/2) and Li2 at 1f (0 1/2 1/2) are half occupied, this induces two different structural models, (i) a disordered structure similar to the monoclinic O3−Li0.5CoO2 (C2/m) and/or (ii) an ordered structure corresponding to an a5 × b5 × 2c5 superstructure in which both Li1/◻ and Li2/◻ alternate perpendicular to the layers (◻: vacancy). Shao-Horn et al. have been the first to observe superstructure reflections associated with the doubling of the monoclinic 3694



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Figure 12. Theoretical construction of the Li0.33CoO2 structure starting from the O3−LiCoO2 structure. (a) O3−LiCoO2 structure, (b) relationship between the O3−LiCoO2 unit cell and the √3a1 × √3a1 supercell, (c) the √3a1 × √3a1 × c1 supercell, (d) group−subgroub transformation from P3̅1m to C2/m-type III, (e) O3−LiCoO2-C2/m-type III supercell. The deintercalation of 2/3 of the lithium atoms, from O3−LiCoO2, the LiCoO2 √3a1 × √3a1 × c1 supercell, and the LiCoO2-C2/m-type III supercell leads to the disordered (f), ordered (g), partially ordered (h), and ordered models (i), respectively.

cell parameter c5. Furthermore, these authors have provided a schematic view of the superstructure and suggested Pm as a

possible space group; however, they did not provide any atomic positions.18 3695



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Figure 13. Structural relationship between LiCoO2-C2/m-type III and Li2MnO3. (a) LiCoO2-C2/m-type III supercell, (b) relationship between LiCoO2-C2/m-type III and LiCoO2-C2/m-type IV supercells, (c) LiCoO2-C2/m-type IV structure, (d) relationship between LiCoO2-C2/m-type IV ⃗ . and LiCoO2-C2/m-type V, (e) LiCoO2-C2/m-type V, and (f) comparison of LiCoO2-C2/m-type V and Li2MnO3 after applying an origin shift 1/2 b11 Theoretical construction of the Li0.33CoO2 structure starting from LiCoO2: (g) Li0.33CoO2-C2/m-type III, (h) Li0.33CoO2-C2/m-type IV, and (i) Li0.33CoO2-C2/m-type V. For the three Li0.33CoO2 structures, well-ordered Li/vacancy models, as previously predicted, are observed.

4.3. From O3−Li0.75CoO2 (R3̅m) to Monoclinic O3− Li0.5CoO2 (P21/m). For an accurate analysis of the a5 × b5 × 2c5 superstructure, this latter has been rebuilt. Starting from the monoclinic O3−LiCoO2 (P2/m) structure (Figure 8), we have first doubled the cell parameter c5 and determined the atomic positions, then lowered the symmetry to P1 (Figure 10a) and ordered the Li and vacancies (Figure 10b) as proposed by ShaoHorn et al.18 Using the PLATON suite of crystallographic programs,30 we have determined that a higher symmetry exists with the space group P21/m. In order to get the final structural model for the space group P21/m, first the unit cell is transformed using the matrix (100,01̅0,1̅01̅), then an origin shift of 1/4 −1/4 0 is applied in order to shift the mirror plan m ⊥b at y = 1/2 to y = 1/4 and the 2-fold screw axis 21 ∥ b at x = 3/4 and z = 0 to x = 0 and z = 0 (Figure 10c). By introducing the space group P21/m, the atomic positions Li2, Co1, Co3, O1, O2, O3, and O4 become equivalent to Li3, Co2, Co4, O7, O8, O6, and O5, respectively (Figure 10d).

The cell parameters and the atomic positions have been optimized based on the single crystal data of O3−Li0.5CoO228 (Figure 10e). Starting from the O3−LiCoO2 layered structure (R3̅m, a1 = 2.8166 Å, and c1 = 14.0452 Å), it is very easy to explain the formation of the O3−Li0.5CoO2 layered supercell (P21/m, a7 = 4.865 Å, b7 = 2.809 Å, c7 = 9.728 Å, and β7 = 99.59°). As previously explained, it is possible to decrease the symmetry from R3m ̅ to C2/m and then to P2/m (a5 = 4.8785 Å and b5 = 2.8166 Å, c5 = 4.9561 Å, β5 = 109.15°) after the deintercalation of 0.5 lithium atoms. Since, the Li1 at 1g (1/2 0 1/2) and Li2 at 1f (0 1/2 1/2) atomic positions could be both half occupied (Figure 8), an ordered structure corresponding to an a5 × b5 × 2c5 supercell, in which both Li1/◻ and Li2/◻ (◻: vacancy) alternate perpendicular to the layers, may form (Figure10b). 5. Theoretical Structure of O3−Li0.33CoO2 and Relationship between O3−LiCoO2 and Li2MnO3 Structures. For the compositions Li0.33CoO2 and Li0.33NiO2, a √3a1 × √3a1 supercell associated with lithium and vacancy ordering, as shown in Figure 11, has been reported;18,31 however, no full 3696



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Figure 14. Construction of a supercell structure common to Li0.5CoO2 (P2/m, a5 = 4.8785 Å, b5 = 2.8166, Å, c5 = 4.9561 Å, β5 = 109.15°) and to Li0.33CoO2 (C2/m-type V, a11 = 4.8784 Å and b11 = 8.4498 Å, c11 = 4.956 Å, β11 = 109.15°) for an accurate determination of the phase transition mechanism from x = 0.5 to x = 0.33.

atomic position empty and the 1b and 2d atomic positions fully occupied (Figure 12g). This configuration is discarded, since it is in contradiction with the previous results, which clearly show that the lithium is extracted from all the layers (see P2/m-Li0.5CoO2 structure). One may obtain a partially ordered Li0.33CoO2 structure if the 6k atomic position is 1/3 occupied (statistical disorder) and the 2d atomic position is empty. This leads to two disordered and one ordered lithium layer, respectively (Figure 12h). From a crystallographic point of view, in order to obtain a well ordered lithium and vacancies in the Li0.33CoO2 structure, the symmetry should be decreased from P3̅1m to C2/m-type III, a9 = 4.8784 Å, b9 = 8.4498 Å, c9 = 14.0452 Å, and β = 90° (a9⃗ = a8⃗ , b9⃗ = a⃗8 + 2b8⃗ , and c9⃗ = c8⃗ , see Figure 12d). This translationengleiche transition of index 3 induces the splitting of the 6k to 8j and 4i atomic positions, whereas 1b and 2d are transformed to 2c and

structural model has been provided. Therefore, starting from the O3−LiCoO2 (R3m ̅ , a1 = 2.8166 Å and c1 = 14.0452 Å) structure (Figure 12a), we have built the √3a1 × √3a1 × c1 supercell and determined 36 atomic positions with considering the space group P1 (Figure 12b). Then, with the PLATON suite of crystallographic programs, we have determined that a higher trigonal symmetry exists with the space group P31̅ m, a8 = b8 = √3a1= 4.8784 Å, c8 = c1 = 14.0452 Å (a8⃗ = a1⃗ − b1⃗ , b8⃗ = a1⃗ + 2b1⃗ , and c8⃗ = c1⃗ , see Figure 12b). By transforming P1 to P3̅1m, we decreased the number of atoms to 10, which led to the structural model depicted in Figure 12c. One should point out that in this structure there are three lithium layers; two with Li occupying the 6k (0.33 0.33 0.166) atomic position and one with Li occupying the 1b (0 0 1/2) and 2d (1/3 2/3 1/2) atomic positions. This suggests that the only possibility to obtain an ordered Li0.33CoO2 structure, using the space group P3̅1m, is to consider the 6k 3697



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Figure 15. Phase transition mechanism from Li0.5CoO2 (P2/m, a5 = 4.8785 Å, b5 = 2.8166, Å, c5 = 4.9561 Å, β5 = 109.15°) (a) to Li0.33CoO2 (c). The red arrows indicate the shift direction of the lithium atoms after the extraction of 0.1667 lithium atoms from Li0.5CoO2 (P2/m) (b). The final Li0.33CoO2 structure may have a monoclinic, an orthorhombic, or a hexagonal unit cell. The green and the blue lines correspond to the √3a1 × √3a1 and √3a1 × 3a1 supercells, respectively (c).

Figure 16. Phase transition mechanism from Li0.33CoO2 (P2/m-type V) (a) to Li0.25CoO2 (R3̅m, a13 = 5.6332 Å, and c13 = 14.0452 Å) (d). The red crosses correspond to the removed Li3 atoms after the extraction of 0.08 lithium atoms from Li0.33CoO2 (P2/m-type V) (b). The red arrows indicate the shift from Li4 to Li1 atomic position (b). The result of the ordering of Li1 and Li3 in successive unit cells (c and d).

The C2/m-type III cell (a9 = 4.8784 Å, b9 = 8.4498 Å, c9 = 14.0452 Å, and β9 = 90°) can be transformed to C2/m-type IV (a10 = 4.8784 Å, b10 = 8.4498 Å, c10 = 14.868 Å, and β10 = 109.15°; ⃗ = b9⃗ , and c1⃗ 0 = c9⃗ − a9⃗ Figure 13c) using the relations: a1⃗ 0 = a9⃗ , b10 (Figure13b). The careful examination of the C2/m-type IV cell shows that it is an isomorphic enlarged unit cell of the Li2MnO3

4h, respectively (Figure 12e). If the lithium atoms at 8j and 4h are extracted, the Li0.33CoO2 composition is obtained and a Li/ vacancy (ratio 1:2) ordering is observed within all the Li layers (Figure 12i). These structural models (Figure 12e,i) are strongly related to the Li2MnO3 structure. The structural relationship is detailed in Figure 13. 3698



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Figure 17. Experimental and theoretical structures of the LixCoO2 phases (0.25 ≤ x ≤ 1).

unit cell (Figure 13d; C2/m-type V, a12 = 4.9261 Å ≈ a10, b12 = 8.5270 Å ≈ b10, c12 = 5.0280 Å ≈ 1/3 × c10, and β12 = 109.22°32). Only dividing the cell parameter c10 by 3 (Figure 13e) and applying an origin shift of 1/2b⃗11 are needed to transform this C2/m-type IV supercell to a C2/m-type V subcell similar to Li2MnO3 (Figure 13f). In addition to the four Li0.33CoO2 structures, depicted in Figure 12f−i, one may build two other structural models starting from LiCoO2 C2/m-type IV and C2/ m-type V. Indeed, the extraction of Li2 at 4h (0 0.166 1/2) and Li3a at 8j (0.0 0.166 0.166) from LiCoO2 C2/m-type IV and Li1 at 4h (0 0.333 1/2) from LiCoO2 C2/m-type V lead to two wellordered Li0.33CoO2 structures, as depicted in Figure 13h and i, respectively. The Li0.33CoO2 model depicted in Figure 12f should be considered as an average structure. It does not take into account the Li and vacancy ordering that lead to the formation of a √3a1 × √3a1 supercell, observed by TEM. The five steps to transform O3−LiCoO2 to the Li2MnO3 structure [(12a) → (12c) → (12e) → (13c) → (13e) → (13f)] can be reduced to three steps [(14a) → (14b) → (14c = 13e) → (13f)]. First, the symmetry is deceased from R3m ̅ to C2/m-type I using the equations a5⃗ = 2a1⃗ + b1⃗ , b5⃗ = −b1⃗ , and c5⃗ = −1/3(2a1⃗ + b⃗1 + c1⃗ ); then, an isomorphic enlarged unit cell C2/m-type V is ⃗ = 3b5⃗ , c1⃗ 1 = c5⃗ , and β11 = β5 built using the equations a⃗11 = a5⃗ , b11 (a11 = 4.8785 Å, b11 = 8.4498 Å, c11= 4.9561 Å, and β11 = 109.15°). This C2/m-type V supercell is similar to the Li2MnO3 cell (C2/m, a12 = 4.9261 Å, b12 = 8.5270 Å, c12 = 5.0280 Å, and ⃗ is needed to obtain β12 = 109.22°32). Only an origin shift 1/2b11 comparable atomic positions (see details in Figure 13e−f).

6. Transformation Mechanism from O3−Li0.5CoO2 to O3−Li0.33CoO2 Structure. In order to determine the phase transition mechanism from the Li0.5CoO2-P2/m to Li0.33CoO2 structure, it is essential to find a common supercell to both structures, which enable the comparison of the different atomic positions. Starting from LiCoO2 (C2/m-type V; Figure 14c or 13e), it is possible to obtain an ordered Li0.33CoO2 (C2/m-type V) structure if the lithium at the 4h (0 0.1667 1/2) atomic position is extracted. However, it is not possible to obtain an ordered Li0.5CoO2 (C2/m-type V) structure unless there is a loss of the centring translations [transformation (14c) → (14d)]. In this transformation, the 4h (0 0.1667 1/2) and 2d (1/2 0 1/2) atomic positions are split to 2k (0 0.1667 1/2) and 2l (1/2 0.333 1/2) and to 1f (0 1/2 1/2) and 1g (1/2 0 1/2), respectively. When the lithiums at 2k and 1f atomic positions are extracted, the ordered Li0.5CoO2 (P2/m-type V) structure is obtained (Figure 14f). The Li0.5CoO2 (P2/m-type V) cell is a supercell of Li0.5CoO2-P2/m [the transformation (14a)→(14b)→(14e) leads to the formation of Li0.5CoO2-P2/m (see more details in section 4.2)]. As shown in Figure 14e and f, the arrangements of lithium and vacancies are exactly the same in both structures. The only difference is in the unit cell parameters (a5 = a11 = 4.8785 Å, b5 = 1/3 × b11 = 2.8166 Å, c5 = c11= 4.9561 Å, and β5 = β11 = 109.15°). When the lithiums at 2k and 2l atomic positions are extracted, the ordered Li0.33CoO2P2/m-type V structure is obtained (Figure 14g). In this structure, the arrangement of lithium and vacancies has been chosen in agreement with the previously predicted models of Figure 11. The comparison of the lithium atomic positions in both 3699



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Li0.5CoO2-P2/m-type V and Li0.33CoO2-P2/m-type V structures indicates that the phase transition, occurring after the deintercalation of 0.1667 Li atoms, is due to the migration of Li2 at 2l (1/2 0.333 1/2) to Li3 at the 1f (0 1/2 1/2) atomic position. On the basis of the above observation, we propose the mechanism of phase transition from Li0.5CoO2-P2/m (Figure 15a) to Li0.33CoO2 (Figure 15c). First, 0.1667 Li is extracted, and then Li shifts to the vacancies indicated by red arrows (Figure 15b). The resulting new cell may be monoclinic, orthorhombic (blue line), or hexagonal (green line) (Figures 12f−i and 13h,i). Indeed, the theoretical powder patterns of these six structural models of Li0.33CoO2 are very similar (Figure S1 of Supporting Information). Only Li0.33CoO2 C2/m-type V and P31̅ m-type I show very weak superstructure reflections, which could not be seen using conventional X-ray diffractometers. 7. Transformation Mechanism from Li0.33CoO2 to O3− Li0.25CoO2 Structure. For simplicity reasons, Li0.33CoO2-P2/mtype V (Figure 16a) will be used as a starting model from which Li would be extracted. When 0.08 Li is extracted, the Li3 atomic position at 1f (0 1/2 1/2) becomes half occupied. Therefore, in two successive unit cells, Li3 is once fully occupied and once empty (Figure 16b). The empty positions are represented by a red cross. It is expected also that Li4 shifts from 1g (1/2 0 1/2) to 2k (0 0.1667 1/2). This shift is indicated by red arrows (Figure 16b). Since the Li1 atomic position is now half occupied, in two successive unit cells Li1 is once fully occupied and once empty. The result of the ordering of Li3 and Li1 is depicted in Figure 16c. From these transformations, a final hexagonal supercell (R3̅m, a13 = 5.6332 Å, c13 = 14.0452 Å) is induced with a structure related to Li0.75CoO2 (Figure 16d). Indeed, in Li0.75CoO2, the atomic positions 9d and 3b, which were full and empty, respectively, become in Li0.25CoO2 empty and full, respectively. Additional TEM experiments have to be performed in order to confirm the presence of such a supercell in Li0.25CoO2. The transformation mechanism proposed here can be applied to the nickel system, since for Li0.33NiO2 and Li0.25NiO2 structures, √3a1 × √3a1 and 2a1 × 2a1 supercells have been observed, respectively.31 As explained in section 5 (theoretical structure of O3−Li0.33CoO2), the Li0.33NiO2 cell could be a hexagonal √3a1 × √3a1 × c1 supercell with a partially ordered structure or most probably an orthorhombic √3a1 × 3a1 × c1 supercell with a monoclinic symmetry and a well ordered structure, as Li0.33CoO2-C2/m-type III (Figure 12i).

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CONCLUSION

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ASSOCIATED CONTENT

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (H.B.Y.). *E-mail: [email protected] (M.S.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was financially supported by the Japan Society for the Promotion of Science (JSPS) Fellows Grant Number 24·02506.

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REFERENCES

(1) Johnston, W. D.; Heikes, R. R.; Sestrich, D. J. Phys. Chem. Solids 1958, 7, 1−13. (2) Mizushima, K.; Jones, P. C.; Wiseman, P. J.; Goodenough, J. B. Mater. Res. Bull. 1980, 15, 783−789. (3) Koksbang, R.; Barker, J.; Shi, H.; Saidi, M. Y. Solid State Ionics 1996, 84, 1−21. (4) Wohlfahrt-Mehrens, M.; Vogler, C.; Garche, J. J. Power Sources 2004, 127, 58−64. (5) Zhang, Y.; Chung, C. Y.; Sun, L. X.; Zhua, M. Mater. Chem. Phys. 2008, 107, 254−260. (6) Aurbach, D.; Markovsky, B.; Rodkin, A.; Levi, E.; Cohen, Y. S.; Kim, H.-J.; Schmidt, M. Electrochim. Acta 2002, 47, 4291−4306. (7) Amatucci, G. G.; Tarascon, J. M.; Klein, L. C. Solid State Ionics 1996, 83, 167−173. (8) Cai, C.; Wang, Y. Mater. 2009, 2, 1205−1238. (9) Wang, H.; Jang, Y.-I.; Huang, B.; Sadoway, D. R.; Chiang, Y.-M. J. Electrochem. Soc. 1999, 146, 473−480. (10) Wang, H.; Jang, Y.-I.; Huang, B.; Sadoway, D. R.; Chiang, Y.-M. J. Power Sources 1999, 81−82, 594−598. (11) Gabrisch, H.; Yazami, R.; Fultz, B. J. Power Sources 2003, 674, 119−121. (12) Gabrisch, H.; Yazami, R.; Fultz, B. J. Electrochem. Soc. 2004, 151 (6), A891−A897. (13) Sharma, N.; Peterson, V. K.; Elcombe, M. M.; Avdeev, M.; Studer, A. J.; Blagojevic, N.; Yusoff, R.; Kamarulzaman, N. J. Power Sources 2010, 195, 8258−8266. (14) Amatucci, G. G.; Tarascon, J. M.; Klein, L. C. J. Electrochem. Soc. 1996, 143 (3), 1114−1123. (15) Abea, T.; Koyama, T. CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 2011, 35, 209−218. (16) Reimers, J. N.; Dahn, J. R. J. Electrochem. Soc. 1992, 139 (8), 2091−2097. (17) Ohzuku, T.; Ueda, A. J. Electrochem. Soc. 1994, 141 (11), 2972− 2977. (18) Shao-Horn, Y.; Levasseur, S.; Weill, F.; Delmas, C. J. Electrochem. Soc. 2003, 150 (3), A366−A373. (19) Gummow, R. J.; Liles, D. C.; Thackeray, M. M. Mater. Res. Bull. 1993, 28, 235−246. (20) Van der Ven, A.; Aydinol, M. K.; Ceder, G. Phys. Rev. B 1998, 58 (6), 2975−2987. (21) Mukai, K.; Nozaki, H.; Ikedo, Y.; Sugiyama, J.; Ariyoshi, K.; Ohzuku, T. J. Power Sources 2009, 192, 684−688. (22) Yang, X. Q.; Sun, X.; McBreen, J. Electrochem. Commun. 2000, 2, 100−103. (23) Clémençon, A.; Shao-Horn, Y. In-situ and Ex-situ Observations of Lithium De-intercalation from LiCoO2: Atomic Force Microscopy and Transmission Electron Microscopy Studies. Master’s thesis, Massachusetts Institute of Technology, Cambridge, MA, 2005. (24) Catti, M. Phys. Rev. B 2000, 61 (3), 1795−1803. (25) Kang, K.; Ceder, G. Phys. Rev. B 2006, 74, 094105−1−094105−7. (26) Van der Ven, A.; Ceder, G. Electrochem. Solid-State Lett. 2000, 3 (7), 201−304. (27) Choi, S.; Manthiram, A. J. Electrochem. Soc. 2002, 149 (9), A1157−A1163.

On the basis of previously reported TEM, XRD, and ND experiments, we have been able to build, for the first time, theoretical crystal structure models for the O3−LixCoO2 supercells (x = 0.75, 0.5, 0.33, and 0.25) (Figure 17). The use of group−subgroup schemes in the Bärnighausen formalism was the key for the determination of the phase transition mechanisms from O3−LiCoO2 to O3−Li0.25CoO2 and from O3−LiCoO2 to the spinel−Li0.5CoO2 structure. Furthermore, it enabled us to conclude that only three steps are required to transform O3− LiCoO2 to the Li2MnO3 type structure. S Supporting Information *

The theoretical powder patterns of Li0.33CoO2 (Figure S1). This information is available free of charge via the Internet at http:// pubs.acs.org/. 3700



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(28) Takahashi, Y.; Kijima, N.; Tokiwa, K.; Watanabe, T.; Akimoto, J. J. Phys.: Condens. Matter 2007, 19, 436202/1−436202/12. (29) Chiang, Y.-M.; Wang, H.; Jang, Y.-I. Chem. Mater. 2001, 13, 53− 63. (30) Spek, A. L. PLATON, A Multipurpose Crystallographic Tool; Utrecht University: Utrecht, The Netherlands, 2008. (31) Delams, C.; Ménétrier, M.; Groguennec, L.; Levasseur, S.; Pérès, J. P.; Pouillerie, C.; Prado, G.; Fournès, L.; Weill, F. Int. J. Inorg. Mater. 1999, 1, 11−19. (32) Strobel, P.; Lambert-Andron, B. J. Solid State Chem. 1988, 75, 90− 98. (33) Hertz, J. T.; Huang, Q.; McQueen, T.; Klimczuk, T.; Bos, J. W. G.; Viciu, L.; Cava, R. J. Phys. Rev. B 2008, 77, 075119/1−075119/12. (34) Motohashi, T.; Ono, T.; Sugimoto, Y.; Masubuchi, Y.; Kikkawa, S.; Kanno, R.; Karppinen, M.; Yamauchi, H. Phys. Rev. B 2009, 80, 165114/1−165114/9. (35) Kawasaki, S.; Motohashi, T.; Shimada, K.; Ono, T.; Kanno, R.; Karppinen, M.; Yamauchi, H.; Zheng, G.-Q. Phys. Rev. B 2009, 79, 220514(R)/1−220514(R)/4.

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NOTE ADDED AFTER ASAP PUBLICATION This article was published ASAP on September 9, 2013, with errors in the caption of Figure 12. The corrected version was reposted on September 12, 2013.

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